Modal analysis of a structure in a compressible fluid using a finite element boundary element approach

One approach to modeling the resonant behavior of structures in a compressible fluid is to use finite elements to describe the structure and boundary elements to describe the fluid. The fluid loading is characterized by a complex, frequency-dependent influence matrix that is combined with the frequency-independent stiffness and mass matrices obtained from the finite element model. This approach works well for determining the fluid-loaded harmonic response of the structure over a specified frequency range, if one knows the appropriate frequency range over which to perform the analysis. Since the in-fluid resonance frequency is usually not known, the designer must choose successive frequency sets until the resonance peak is found. This paper describes a method that eliminates this guesswork by computing the in-fluid eigenfrequency of the mode of interest using boundary elements to model the fluid loading. The procedure is iterative; beginning with the in vacuo eigenfrequency and continuing until the in-fluid eigenvalue converges. The designer may then perform a harmonic analysis in a narrow band about the computed eigenfrequency to obtain the structural and/or acoustic response levels. The accuracy and efficiency of the technique is demonstrated with two examples: a spherical shell and a low-frequency projector, both in water.